Ulrika is the Swedish form of Ulrike — from the Germanic uodal (heritage, prosperity) + rīhhi (ruler). Princess Ulrika — Swedish royal heritage naming.
Ulrika does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Ulrika reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.